Analysis of compressible potential flow over aerofoils using the dual reciprocity method

Abstract

Abstract The use of the linearised potential model for the analysis of compressible flows is quite widespread, and provides good results for subsonic and supersonic flows. However, the calculation of aerofoils and wings subject to transonic flows requires a non-linear model, such as the transonic small-disturbance (TSD) potential equation. The solution of the problem by a singularity distribution requires singularities over the field, as well as panels on the boundary, characterising the procedure known as field panel method. The present work shows results of calculations of the transonic small-disturbance potential equation for flows without shock waves using the dual reciprocity method (DRM), which permits calculation of integrals only at the boundary of the problem, without the need of field distributions. This approach, compared to the field panel methods, takes considerably less computer time, and shows a significant improvement when compared to results of linear theory without much additional computer time, making this technique adequate to design phases of aircraft. Pressure distribution results show good agreement with other methods found in litterature. The low computational cost of the present method allows us to perform parametric tests and explore the effects of thickness and Mach number on the lift and pitching moment coefficients. A discussion of the physical effect of these parameters on the problem is presented, and the thickness of the aerofoil is shown to increase the lift and change the position of the aerodynamic centre. However, this non-linear effect depends on the precise shape of the thickness distribution.